库尔沙克铰接拼图证明：正十二边形与正方形对应

GeoGebra 命令及参数

1. Point(xAxis) → A
2. Rotate(A, (360° * 1 / 12)) → A_1
3. Polygon(A, A_1, 12) → poly1, f, p_{2}, q, r, B, C, D, E, F, G, H, g, I, J, K, h, i, j, k, l, m, n
4. Polygon(A, A_1, 3) → poly2, s, t, a, L
5. Polygon(O, A, L) → t1, l_1, o, a_1
6. Polygon(O, A_1, L) → t2, l_2, o_1, b
7. Polygon(A_1, B, 3) → poly3, c, d, e, M
8. Polygon(B, C, 3) → poly4, f_1, g_1, h_1, N
9. Polygon(O, A_1, M) → t3, m_1, o_2, i_1
10. Polygon(O, M, B) → t4, b_1, o_3, m_2
11. Polygon(O, N, B) → t5, b_2, o_4, n_1
12. Polygon(O, N, C) → t6, c_1, o_5, n_2
13. Flatten(Sequence[Rotate[l1, (k * 90°)], k, 1, 3]) → l2
14. OrthogonalLine(A, xAxis) → j_1
15. OrthogonalLine(C, yAxis) → k_1
16. Intersect(j_1, k_1) → P
17. Mirror(P, xAxis) → P'
18. Polygon(P', P, 4) → poly5, q_1, r_1, s_1, t_1, Q, R
19. Rotate(O, ((-p(u)) * 270°), A) → O'
20. Rotate(A, ((-p(u)) * 270°), A) → A'
21. Rotate(L, ((-p(u)) * 270°), A) → L'
22. Polygon(O', A', L') → t1', l', o', a'
23. Polygon(L', A, 3) → poly6, p_1, d_1, e_1, S
24. Mirror(A, a') → A'_{1}
25. Rotate(S, (p(u) * 60°), O') → S'
26. Rotate(L', (p(u) * 60°), O') → L''
27. Polygon(O', L'', S') → t7, s', f_2, l''
28. Mirror(L'', l'') → L'''
29. Rotate(L''', (p(u) * (-360 + 180)°), S') → T
30. Rotate(O', (p(u) * (-(180°))), S') → O''
31. Polygon(O'', S', T) → t8, t_2, o'', g_2
32. Polygon(T, S', 3) → poly7, h_2, i_2, j_2, U
33. Rotate(U, (p(u) * 150°), T) → U'
34. Rotate(S', (p(u) * 150°), T) → S''
35. Polygon(U', T, S'') → t9, s'', u', t_3
36. Rotate(U, (p(u) * 60°), O'') → SS
37. Rotate(T, (p(u) * 60°), O'') → T'
38. Polygon(O'', T', SS) → t10, u'_{1}, k_2, t'
39. Rotate(O'', (p(u) * (-(180°))), SS) → O'''
40. Rotate(poly6, ((p(u))^(2) * 150°), L') → poly6'
41. LineBisector(O', O'') → q_2
42. LineBisector(O'', O''') → r_2
43. Mirror(poly6', q_2) → poly6''
44. Mirror(O'', r_2) → O'''_{1}
45. Mirror(S', r_2) → S''_{1}
46. Mirror(T, r_2) → T'_{1}
47. Polygon(O'''_{1}, S''_{1}, T'_{1}) → t8', t'_{1}, o'''_{1}, s''_{1}
48. Mirror(O'', r_2) → O'''_{2}
49. Mirror(T', r_2) → T''
50. Mirror(SS, r_2) → SS'
51. Polygon(O'''_{2}, T'', SS') → t10', ss', o'''_{2}, t''
52. Mirror(poly6'', r_2) → poly6'''
53. Rotate(l1, 0°) → l1'
54. Flatten(Sequence[Rotate[{poly2, poly3, poly4}, (k * 90°)], k, 1, 3]) → lt
55. Mirror(poly3, g) → poly3'
56. Flatten(Sequence[Rotate[{poly3'}, (k * 90°)], k, 1, 3]) → l3